A shared online demo can be found at http://demo.redmine.org/. It's been setup to give registered users the ability to create their own projects. This means once you register, you can create your own project on there and try out the project administration features.

Alternatively, you can get your own Redmine demo environment at http://m.redmine.org with full administrator privileges after filling a simple form.

Redmine is built and maintained by community volunteers. If you enjoy using it and would like to give back to the community, the Contribute page has several ideas. Software development experience is not required. Check out the Teams Page if you are interested in a specific area to contribute regularly.